Wouldn’t WordPress do most of what you’re looking for? WordPress supports threaded comments now, so replies to a post take on the shape of a threaded conversation. Also, email notification of replies is built in. What are you looking for in bbPress that WordPress does not offer?

However the threaded replies are not indented as happens with Threaded Comments for Posts. Using the Education Theme and the Genesis Framework. Don’t know what supplies the indenting on threaded Post Comments.